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A240922 Magic constants of associative 4 X 4 X 4 cubes composed of distinct prime numbers.

%I A240922 #21 Jan 09 2021 02:54:00
%S A240922 1260,1320,1380,1428,1440,1500,1560,1596,1620
%N A240922 Magic constants of associative 4 X 4 X 4 cubes composed of distinct prime numbers.
%C A240922 A magic cube is associative if the sum of its any two elements that are symmetric about the cube center equals the same number, called the associativity constant of the cube.
%C A240922 All magic 3 X 3 X 3 cubes are associative.
%D A240922 Andrews W. S. Magic Squares & Cubes, Dover Publ, 1960 (original publication Open Court, 1917)
%D A240922 William H. Benson and Oswald Jacoby. Magic Cubes. New Recreations. 1981.
%D A240922 Gakuho Abe, Related Magic Squares with Prime Elements, JRM 10:2 1977-78, pp.96-97.
%D A240922 A. W. Johnson, Jr., An Order 4 Prime Magic Cube, JRM 18:1, 1985-86, pp 5-7.
%H A240922 Harvey Heinz, <a href="http://www.magic-squares.net/c-t-htm/c_prime.htm">Prime Number Magic Cubes</a>
%H A240922 Natalia Makarova, <a href="/A240922/a240922.txt">Magic cubes corresponding to terms a(1)-a(6)</a>
%H A240922 <a href="http://dxdy.ru/post835370.html#p835370">Discussion in forum dxdy.ru</a> (in Russian)
%H A240922 <a href="http://primesmagicgames.altervista.org/wp/competitions/">Result for Magic Cubes of Prime Numbers</a>
%e A240922 a(1)=1260 corresponds to the following cube:
%e A240922    23 521 433 283
%e A240922   373  29 457 401
%e A240922   587 139  11 523
%e A240922   277 571 359  53
%e A240922   ---------------
%e A240922   263 379 557  61
%e A240922   613  13 131 503
%e A240922   317 449  31 463
%e A240922    67 419 541 233
%e A240922   ---------------
%e A240922   397  89 211 563
%e A240922   167 599 181 313
%e A240922   127 499 617  17
%e A240922   569  73 251 367
%e A240922   ---------------
%e A240922   577 271  59 353
%e A240922   107 619 491  43
%e A240922   229 173 601 257
%e A240922   347 197 109 607
%Y A240922 Cf. A239671.
%K A240922 nonn,more
%O A240922 1,1
%A A240922 _Natalia Makarova_, Aug 02 2014